The continuous memristor models have been applied to various chaotic circuits. However, the discrete memristor models and their applications to discrete maps haven't attracted much attention, yet. In this brief, we first present a discrete memristor model and analyze its characteristics. By coupling the model into the Logistic map, a memristive Logistic map is further achieved. Due to the existence of line fixed point, the memristive Logistic map can be unstable or critically stable, depending on its control parameters and initial state. Using several analysis methods, we study the control parameters-relied dynamical behaviors of the memristive Logistic map and disclose its hyperchaotic attractors. The numerical results show that the discrete memristor can efficiently improve the chaos complexity in the Logistic map. In addition, digital experiments are designed to validate the numerical results.

中文翻译：

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忆阻器耦合 Logistic 超混沌映射


连续忆阻器模型已应用于各种混沌电路。然而，离散忆阻器模型及其在离散映射中的应用尚未引起太多关注。在本文中，我们首先提出一个离散忆阻器模型并分析其特性。通过将模型耦合到Logistic映射中，进一步实现了忆阻Logistic映射。由于线不动点的存在，忆阻Logistic图可能不稳定或临界稳定，具体取决于其控制参数和初始状态。使用多种分析方法，我们研究了忆阻 Logistic 图的依赖于控制参数的动力学行为，并揭示了其超混沌吸引子。数值结果表明，离散忆阻器可以有效提高Logistic图中的混沌复杂度。此外，还设计了数字实验来验证数值结果。